A Method for the Numerical Integration of the Equations of Motion Arising From a Finite-Element Analysis

Abstract

This paper describes an extended de Vogelaere method which can be used to integrate numerically the equations of motion arising from a finite-element analysis. The method has a truncation error of fifth order in the integration step length, and can be easily programmed for a digital computer. More important is that the method requires a minimum amount of computer storage and computer run time compared with other methods commonly used in numerical analysis and, therefore, is particularly useful in solving a large system of equations. The integration technique has been used to study two-dimensional wave propagation in axisymmetric and plane-strain problems. Results are compared with those of the finite difference and the method of characteristics.